4x^2-7x-100=0

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Solution for 4x^2-7x-100=0 equation: 


Simplifying
4x2 + -7x + -100 = 0

Reorder the terms:
-100 + -7x + 4x2 = 0

Solving
-100 + -7x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-25 + -1.75x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -1.75x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -1.75x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1.75x + x2 = 0 + 25
-1.75x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-1.75x + x2 = 25

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 25 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 25 + 0.765625

Combine like terms: 25 + 0.765625 = 25.765625
0.765625 + -1.75x + x2 = 25.765625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 25.765625

Calculate the square root of the right side: 5.075985126

Break this problem into two subproblems by setting 
(x + -0.875) equal to 5.075985126 and -5.075985126.


Subproblem 1
x + -0.875 = 5.075985126

Simplifying
x + -0.875 = 5.075985126

Reorder the terms:
-0.875 + x = 5.075985126

Solving
-0.875 + x = 5.075985126

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = 5.075985126 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = 5.075985126 + 0.875
x = 5.075985126 + 0.875

Combine like terms: 5.075985126 + 0.875 = 5.950985126
x = 5.950985126

Simplifying
x = 5.950985126


Subproblem 2
x + -0.875 = -5.075985126

Simplifying
x + -0.875 = -5.075985126

Reorder the terms:
-0.875 + x = -5.075985126

Solving
-0.875 + x = -5.075985126

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x = -5.075985126 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x = -5.075985126 + 0.875
x = -5.075985126 + 0.875

Combine like terms: -5.075985126 + 0.875 = -4.200985126
x = -4.200985126

Simplifying
x = -4.200985126


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.950985126, -4.200985126}

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